In commonly assigned U.S. Pat. No. 4,968,925 of Rik W.A.A. De Doncker, issued Nov. 6, 1990, a universal field-oriented (UFO) controller is described which allows for field-oriented control of induction machines in an arbitrary flux reference frame. The principle of the UFO controller applies to both direct and indirect field orientation. In practice, this allows for the integration of six different field orientation schemes into a single control, i.e., direct and indirect field orientation in rotor flux, air gap flux and stator flux reference frames. In operation of the UFO controller, a synchronous reference frame is selected by setting the effective stator-to-rotor turns ratio to a predetermined value corresponding thereto. Transitions between reference frames are accomplished by changing the turns ratio. The result is complete decoupling of torque and flux in a flexible, simple and robust drive that is relatively insensitive to machine parameters. U.S. Pat. No. 4,968,925 is incorporated by reference herein.
A problem in direct field orientation is that sensed direct (d) and quadrature (q) components of flux must be processed to an angle to be useful for the vector rotator of the field oriented controller which transforms the coordinates of a vector from one reference frame to another. This involves a Cartesian-to-polar (C/P) coordinate transformation that requires many processor instruction cycles. In particular, the dq coordinates of a flux space vector .PSI. are represented as .PSI..sub.d and .PSI..sub.q, and the C/P transformation formulas are: ##EQU1## where .PSI. is the amplitude and .delta. is the angle of the flux space vector.
Conventionally, the square root function and the arc tangent function in C/P transformations are performed with either look-up tables or by iterative approximations. Alternatively, the square root function may be processed using a sequential square root algorithm. Disadvantageously, such functions take too much time for high speed drives.
Therefore, it is desirable to provide a method for quickly and accurately determining the amplitude and angle components of flux for use in a field-oriented control scheme.